Short story about space zombies

I'm trying to find a sci-fi short story. Unfortunately, I do not remember anything about the author or title. It is at least a decade or two old, available for free online.

The entire story is set aboard a starship in deep space, and everyone has advanced technology (nanomachines?) that can repair tissue damage that would normally be deadly. Unfortunately, the ship is hit by a massive radiation burst, nearly killing everyone aboard, causing all kinds of damage, and contaminating much of what's left. Somehow, the worst affected have massive brain damage, and the nanomachines are driving them to instinctively seek raw materials for repairs--which can only be found in the brains of relatively intact survivors.

In short, the whole setup is basically an excuse to have space zombies. The nanomachines keep them alive even when their organs are falling out, but they're dumb and slow and they want braaaaains.

Other things I remember:

• The protagonist is female, and was protected by the initial burst because she was working inside a large water tank.
• The protagonist is trying to help her romantic partner, who is comatose, but it's implied they might wake up as a zombie.
• The protagonist is trying to avoid killing the zombies when possible, because there is still a chance of curing them.
• The protagonist is looking for raw materials that aren't radiation-contaminated, to help her partner and repair the ship.